Calling variable functions based on name
Put references to the functions in a dictionary, using the names you want to invoke them by as keys, and the references as value.

functions={"A":DrawA, # The function name *must not* be followed by parentheses
"B":DrawB,
"C":DrawC
}


Then, you only have to check if type is in the dictionary, and call the function using functions[type](...).

(Edited for clarity in regard to the lack of parentheses)